NASA Logo - Web Link to NASA.gov

+ Text Only Site
+ Non-Flash Version
+ Contact Glenn

Go
ABOUT NASA NEWS AND EVENTS MULTIMEDIA MISSIONS MyNASA WORK FOR NASA
Computer Drawing of tow trajectories; one for an impulsive
 side force, one for a centralized side force.

Sir Isaac Newton first presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis" in 1686. His first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. When an external force F is applied, the object is accelerated a in the direction of the force with a magnitude directly proportional to the force and inversely proportional to the mass m of the object. This is a restatement of Newton's second law of motion:

a = F / m

On this page we show two examples of the motion of an object which is subjected to a single external side force. In both cases, we are viewing the motion from above. An object, represented by a black circle, enters the domain from the bottom while moving at a constant initial velocity V. The small black circles represent the position of the object as time passes; the red line is the path, or trajectory, of the object's motion. There is initially no external force acting on the object, so in keeping with Newton's first law, the object moves upward at a constant velocity. The object is then subjected to a side force F.

Trajectory A - Instantaneous Force

On the left side of the figure, the force F is directed to the right of the path and is instantaneously applied to the object. This type of force application occurs if the object experiences a collision with another object moving to the right. In response to Newton's second law, the object receives an instantaneous acceleration to the right; the velocity to the right is changed from zero to some new value. Remember that forces, accelerations, and velocities are vector quantities having both a magnitude and a direction and that the acceleration of an object in response to an external force is in the direction of the force. Since the force is instantly removed, the object continues in a straight line motion as described by the first law. The object now has an additional component of velocity (to the right) which remains until some future external force acts on the object.

Trajectory B - Continuous Force

On the right side of the figure, the force F is directed to the right of the path and is continuously applied to the object. This type of force application occurs if the object is subjected to an aerodynamic side force which is perpendicular to the flight direction, such as the banking turn of an aircraft, or a thrown, spinning ball. If the force remains constant, and is applied perpendicular to the motion, the resulting path is a circular arc. The radius of the circle is called the radius of curvature - R and it depends on the relative magnitude of the velocity V and the acceleration a generated by the side force.

R = V ^2 / a

When the force is removed (banked aircraft brought to wings level) the object continues in a straight line motion as described by the first law. A continuous force applied perpendicular to the motion is called a centralized force since it produces a circular motion about some central point.


Activities:

Button to Display Grade 9-12 Activity

Guided Tours
  • Button to Display Previous Page Forces, Torques and Motion: Button to Return to Guided Tour Page
  • Button to Display Previous Page Banking Turn: Button to Return to Guided Tour Page


Navigation ..

Button to Display Aerodynamics Index Button to Display Model Rocket Index
Beginner's Guide Home Page

 

     First Gov Image


+ Inspector General Hotline
+ Equal Employment Opportunity Data Posted Pursuant to the No Fear Act
+ Budgets, Strategic Plans and Accountability Reports
+ Freedom of Information Act
+ The President's Management Agenda
+ NASA Privacy Statement, Disclaimer,
and Accessibility Certification

 

NASA Logo   
Editor: Nancy Hall
NASA Official: Nancy Hall
Last Updated: May 05 2015

+ Contact Glenn